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          Streaming MultiProcessor、Register、Shared-Memory对线程块尺寸的影响
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        <h2 id="简介"><a href="#简介" class="headerlink" title="简介"></a>简介</h2><p>线程块中线程总数的大小除了受到硬件中<code>Max Threads Per block</code>的限制，同时还要受到<code>Streaming Multiprocessor、Register</code>和<code>Shared Memory</code>的影响。这些条件的共同作用下可以获得一个相对更合适的<code>block</code>尺寸。当<code>block</code>尺寸太小时，将无法充分利用所有线程；当<code>block</code>尺寸太大时，如果线程需要的资源总和过多，<code>CUDA</code>将通过强制减少<code>block</code>数量来保证资源供应，同样无法利用所有线程。而<code>grid</code>的尺寸通常越大越好，当然够用就可以了，以免浪费资源。  </p>
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<p>本文需要通过<code>NVIDIA</code>官方提供的一个非常有用的工具<code>C:\Program Files\NVIDIA GPU Computing Toolkit\CUDA\v7.0\tools\CUDA_Occupancy_Calculator.xls</code>进行辅助计算来获得合适的<code>block</code>大小。这个<code>excle</code>表中的<code>Help</code>表单有详细的使用说明，以下分析将基于这个工具。<br>可以通过在编译时添加<code>--ptxas-options=-v</code>参数在编译时输出当前程序中所使用的<code>Register</code>和<code>Shared Memory</code>大小。</p>
<h2 id="SM的限制对block尺寸的影响"><a href="#SM的限制对block尺寸的影响" class="headerlink" title="SM的限制对block尺寸的影响"></a>SM的限制对block尺寸的影响</h2><p><code>Multiprocessor</code>(以下所有的<code>Multiprocessor</code>都是指<code>Streaming Multiprocessor</code>，即SM,具体SM在GPU中的结构组织参见<a href="http://notes.maxwi.com/2015/06/11/CUDA-study-notes/">http://notes.maxwi.com/2015/06/11/CUDA-study-notes/</a>基本概念中的图示)中<code>thread</code>数量的限制主要影响工作状态的线程是否能够占满当前的整个<code>Multiprocessor</code>。为了使工作状态的线程能够占满整个<code>Multiprocessor</code>，<code>block</code>中的<code>thread</code>的总数应当不小于<code>Max Threads Per Multiprocessor / Max Thread Blocks Per Multiprocessor</code>。</p>
<p>下图所示为CUDA_Occupancy_Calculator给出的计算能力为5.0的GPU的参数。<br><img data-src="1.png" alt="Physical Limits for GPU Compute Capability">  </p>
<p>此时线程块的中线程数量应当不小于2048/32 = 64。当线程块的数量小于64时，由于每个Multiprocessor中可以含有的最大线程块只有32个，所以此时32个线程块乘以这个小于64的数字必然要小于2048，也就是无论怎样都无法使线程填满整个Multiprocessor，导致SM中会有空闲的Streaming Processor。所以根据要填满SM，则要求每个线程块中至少需要有64个线程。如果将线程块尺寸设置为1024，则此时根据SM总线程的限制2048，每个SM可以启动2个线程块。</p>
<p>注意：1). 当前计算能力5.0的设备每个线程块中线程数量上限Maximum Thread Block Size=1024、2). CUDA中线程组织单位为Wrap，此处Threads per Warp=32，所以线程块中的线程数量应为32的倍数。3). 各维都有大小限制，计算能力5.0的三维分别为1024,1024,64</p>
<h2 id="CUDA-Occupancy-Calculator的使用"><a href="#CUDA-Occupancy-Calculator的使用" class="headerlink" title="CUDA_Occupancy_Calculator的使用"></a>CUDA_Occupancy_Calculator的使用</h2><p>下图为<code>CUDA_Occupancy_Calculator</code>计算结果，由于此处只讨论了SM中线程及线程块的限制对<code>block</code>尺寸的影响，所以这里只需要使曲线的红三角在波峰即可。注意第一张图中的1.)、1.b)需要根据自己的硬件情况进行选择；2).需要自己填入的程序参数(可以通过2.2的方法获得)，3).工具计算出的GPU使用率，显示此时占用为100%，也就是SM中的活动线程束为64个，即64*32。其他各图是其对应的曲线，由第二幅图可以看出在<code>register</code>和<code>shared memory</code>固定的情况下，block尺寸设置为256, 512, 1024时都可以占满SM，因为它们都有以下特点：1). 大于64，满足不小于<code>Max Threads Per Multiprocessor / Max Thread Blocks Per Multiprocessor</code>; 2). 32的整数倍，满足线程束的最小单位Wrap; 3). 可以被2048整除，因为<code>Max Threads Per Multiprocessor=2048</code>。<br><img data-src="2.png" alt="CUDA Occupancy Calculator"><br><img data-src="3.png" alt="Impact of Varying Block Size"><br><img data-src="4.png" alt="Impact of Varying Shared Memory Usage Per Block"><br><img data-src="5.png" alt="Impact of Varying Register Count Per Thread ">  </p>
<h2 id="Register对block尺寸的影响"><a href="#Register对block尺寸的影响" class="headerlink" title="Register对block尺寸的影响"></a>Register对block尺寸的影响</h2><p>计算能力为5.0的设备<code>Registers per Multiprocessor=65536，Max Registers per Thread=256</code>。也就是说一个SM总共也就只有65536个<code>register</code>，一个<code>thread</code>最多能定义256大小的<code>register</code>，根据上图可以看出，显然当<code>Register Per Thread</code>大于32时性能就要开始降低了。因为当前情况下SM中的所有线程都被占满了(此处占满意思是所有线程都为活动线程)，也就是说在这种block参数配置下，一个SM最多可以启动2048个线程(注意是最多可以，并不是说一定要，比如我一共就1000个数据，当然就启动1000个线程就可以了)，由于SM中能使用的register最多只有65536，当SM中的资源不够用时，SM就会强制减少block，所以<code>Register Per Thread</code>应该不大于<code>Registers per Multiprocessor / Max Threads per Multiprocessor</code>，也就是65536 / 2048 = 32</p>
<h2 id="Shared-Memory对block尺寸的影响"><a href="#Shared-Memory对block尺寸的影响" class="headerlink" title="Shared Memory对block尺寸的影响"></a>Shared Memory对block尺寸的影响</h2><p>计算能力为5.0的设备<code>Shared Memory per Multiprocessor (bytes)=65536，Max Shared Memory per Block=49152</code>。也就是说block中的<code>smem(Shared Memory)</code>必须要小于49152，要想使得SM中的线程全部占满，那么整个SM中占用的smem必须小于65536。由于smem是以block为单位进行分配，所以当smem不够用时也就会以block为单位进行减少线程。所以<code>Shared Memory Per Block (bytes)</code>应该不大于<code>Shared Memory per Multiprocessor / Active Thread Blocks per Multiprocessor = Shared Memory per Multiprocessor / (Max Threads per Multiprocessor / Threads Per Block)</code>，当block尺寸设置为256时，<code>Shared Memory Per Block (bytes)</code>最大值为65536 / (2048/256) = 8192。</p>
<h2 id="总结"><a href="#总结" class="headerlink" title="总结"></a>总结</h2><p>block最佳尺寸应该满足：<br>1). 不小于<code>Max Threads Per Multiprocessor / Max Thread Blocks Per Multiprocessor</code>；<br>2). 32的整数倍；<br>3). 可以被<code>Max Threads Per Multiprocessor</code>整除。  </p>
<p>4). <code>Register Per Thread</code>应该不大于<code>Registers per Multiprocessor / Max Threads per Multiprocessor</code>，否则根据<code>CUDA_Occupancy_Calculator.xls</code>参考调节block尺寸以获得最佳性能。  </p>
<p>5). <code>Shared Memory Per Block (bytes)</code>最大值应该不大于<code>Shared Memory per Multiprocessor / (Max Threads per Multiprocessor / Threads Per Block)</code>，否则根据<code>CUDA_Occupancy_Calculator.xls</code>参考调节block尺寸以获得最佳性能。  </p>
<p>注意：  </p>
<ol>
<li>没有标明单位的量其单位都为个。  </li>
<li><code>CUDA_Occupancy_Calculator</code>给出了<code>register</code>和<code>shared memory</code>的分配单位，精确优化时应该非常有用。<br>Register allocation unit size        256<br>Register allocation granularity        warp<br>Shared Memory allocation unit size  256<br>Warp allocation granularity         4   </li>
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